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Learning KPZ Dynamics.
Rel. Alfredo Braunstein, Alberto Rosso, Sergio Chibbaro, Cyril Furtlehner. Politecnico di Torino, Master of science program in Physics Of Complex Systems, 2025
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Abstract
Non-linear stochastic processes are notoriously difficult to model, and inferring the dy- namical equations from observations alone can be extremely challenging. To address this, our work develops an entirely data-driven Neural Network framework that learns a trans- form to linearize the system’s dynamics. This is achieved by mapping the observations onto a latent space where the dynamical evolution is of a linear form. The result is a highly interpretable model, as the learnt transformation can be related to known functions and the dynamics to corresponding linear operators. While neural network-based approaches have demonstrated considerable success in modeling deterministic dynamical systems, ex- tending them to the stochastic regime represents a novel research frontier.
We develop new ideas and validate them on the Kardar-Parisi-Zhang (KPZ) equation, a paradigmatic model for non-linear stochastic growth
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